Answer
$\frac{\sqrt3}{3}$
Work Step by Step
Convert the angle measure to degrees to obtain:
$=\frac{5\pi}{6} \cdot \frac{180^o}{\pi} = 5(30^o)=150^0$
Thus,
$\tan{(\frac{5\pi}{6})}
\\= \tan{150^o}$
150 degrees is in Quadrant II so :
(i) its reference angle is $180^o-150^o=30^o$
(ii) its tangent value is negative
From Section 2.1 (page 50) , we learned that:
$\tan{30^o} = \frac{\sqrt3}{3}$
This means that:
$\tan{150^o} = \tan{30^o} = \frac{\sqrt3}{3}$.
